More recently Haney worked as special effects makeup artist and key makeup artist on the fan made internet series Star Trek: New Voyages episodes In Harms Way (2004), Center Seat (2006), and To Serve All My Days (2006).

In 1990 Haney won the Academy Award for Best Makeup for the drama Driving Miss Daisy which he shared with Manlio Rochetti and Lynn Barber. Further Emmy Awards and nominations Haney earned throughout the years are: an Emmy Award for Outstanding Individual Achievement in Makeup for a Miniseries or a Special in 1992 for Mark Twain, an Emmy Award for Outstanding Individual Achievement in Makeup for a Miniseries or a Special in 1995 for The Show Formerly Known as the Martin Short Show, an Emmy Award for Outstanding Individual Achievement in Makeup for a Miniseries or a Special in 1996 for Kissinger and Nixon, an Emmy Award nomination for Outstanding Makeup for a Miniseries, Movie or a Special in 1999 for The Rat Pack, an Emmy Award for Outstanding Makeup for a Series in 1999 for The X-Files episodes Two Fathers/One Son (shared with Mark Shostrom, Rick Stratton, Jake Garber, Craig Reardon, Steve LaPorte, and Perri Sorel), an Emmy Award for Outstanding Makeup for a Miniseries, Movie or a Special in 2000 for Life with Judy Garland: Me and My Shadows, and an Emmy Award for Outstanding Makeup for a Series (Prosthetic) in 2003 for an episode of Primetime Glick.

In 1993 Haney received a CableACE Award for Best Makeup for his work on Mark Twain and Me, 1992 and 1994 he received BAFTA Film Award nominations for Best Makeup Artist for his work on The Addams Family and Addams Family Values, 1993 he earned a Saturn Award nomination for Best Makeup on Death Becomes Her, 1994 a Saturn Award for Best Makeup on Addams Family Values. In addition, Haney was three times nominated for a Hollywood Makeup Artist and Hair Stylist Guild Award: In 2000 for Best Special Effects Makeup - Feature for Austin Powers: The Spy Who Shagged Me (shared with Ken Myers), 2001 for Best Contemporary Makeup - Television (For a Single Episode of a Regular Series - Sitcom, Drama or Daytime) for the Friends episode The One That Could Have Been, and 2003 for Best Special Makeup Effects - Television Series on the series Primetime Glick

Haney, who started his career in the early '80s, worked on projects such as the horror comedy Basket Case (1982), the horror film Amityville 3-D (1983, with Doug Drexler), Ron Howard's science fiction film Cocoon (1985, with Greg Cannom, Rick Stratton, and Michael Burnett), the horror film Poltergeist III (1988, with Doug Drexler and Mark Shostrom), the comic adaptation Dick Tracy (1990, with Doug Drexler, Anthony Fredrickson, Gilbert A. Mosko, Rolf John Keppler, Ve Neill, Craig Reardon, Mark Shostrom, and Greg Cannom), the sport drama The Babe (1992), the fantasy film Hocus Pocus (1993, with Hazel Catmull and Julia L. Walker), the drama The Shwshank Redemption (1994), Wolfgang Petersen's thriller Air Force One (1997), Ron Howard's fantasy film How the Grinch Stole Christmas (2000), Steven Spielberg's science fiction film Artificial Intelligence: AI (2001), Tim Burton's science fiction remake Planet of the Apes (2001), the science fiction comedy Men in Black II (2002), the fantasy film The Santa Clause 3: The Escape Clause (2006), the television series Medium (2007, with Steven E. Anderson and Todd McIntosh), and the music comedy Walk Hard: The Dewey Cox Story (2007).

In addition to his work behind the scenes, Haney was featured in the specials A Tribute to Dick Smith (1998), Miss Daisy's Journey: From Stage to Screen (2003), Creature People (2007), and He Who Made Monsters: The Life and Art of Jack Pierce (2008). In 2001 he played a Pawn Shop Owner in the comedy I Surrender All.